Four fire engines and around 25 firefighters were called to a fire at block of flats on Victoria Road in Acton.
Part of a kitchen in a flat on the ninth floor was destroyed by fire.
Two men left the property before the Brigade arrived.
The Brigade was called at 1314 and the incident was under control by 1521. Fire crews from Park Royal, Acton, Willesden and Ealing fire stations were at the scene.